= Solution
An isotropic fourth-order tensor has the form $A_{ijkl}=a\delta_{ij}\delta_{kl}+b\delta_{ik}\delta_{jl}+c\delta_{il}\delta_{jk}$. Contracting with the velocity gradient gives $a\delta_{ij}\nabla\cdot u+b\partial_ju_i+c\partial_iu_j$. <Incompressibility> removes the first term. Symmetry of the stress for arbitrary incompressible velocity gradients, including antisymmetric ones, forces $b=c$. Writing their common value as the <dynamic viscosity> $\mu$ yields
$$
\boxed{A_{ijkl}\partial_lu_k=\mu(\partial_ju_i+\partial_iu_j)=2\mu e_{ij}}.
$$
The asserted constant is the homogeneous material coefficient of this Newtonian constitutive law. Isotropy alone fixes its tensor form, not spatial constancy if the material's viscosity were allowed to vary.
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